Problem: The equation of an ellipse $E$ is $\dfrac {(y+9)^{2}}{49}+\dfrac {(x+4)^{2}}{25} = 1$. What are its center $(h, k)$ and its major and minor radius?
The equation of an ellipse with center $(h, k)$ is $ \dfrac{(x - h)^2}{a^2} + \dfrac{(y - k)^2}{b^2} = 1$ We can rewrite the given equation as $\dfrac{(x - (-4))^2}{25} + \dfrac{(y - (-9))^2}{49} = 1 $ Thus, the center $(h, k) = (-4, -9)$ $49$ is bigger than $25$ so the major radius is $\sqrt{49} = 7$ and the minor radius is $\sqrt{25} = 5$.